What are ALL the solutions to the equation on [0,2π)?

csc is   1/sin    in quadrant III   and IV   sin is negative, so there should be two answers'

1/sin = -2 sqrt3/3

sin = 1/(-2 sqrt3/3)

arcsin = -60 degrees    and   240 degrees       or     240 and 300 degrees   or  4pi/3    and  5pi/3     this is   3x

divide the answers by 3     4pi/9   5pi/9      (edited)